Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices

TL;DR

This paper presents a comprehensive multi-orbital mean-field approach to describe quantum phases of bosonic atoms in optical lattices, accurately capturing phase transitions and excitations across interaction regimes.

Contribution

It introduces a unified real-space mean-field method that models various quantum phases and transitions, aligning with many-body results and revealing new localized and excited states.

Findings

Accurate prediction of superfluid to Mott insulator transition in 1D.

Identification of additional Mott insulator phases with localized atoms.

Discovery of on-site excitations as lowest energy excitations.

Abstract

Quantum phases and phase transitions of weakly- to strongly-interacting bosonic atoms in deep to shallow optical lattices are described by a {\it single multi-orbital mean-field approach in real space}. For weakly-interacting bosons in 1D, the critical value of the superfluid to Mott insulator (MI) transition found is in excellent agreement with {\it many-body} treatments of the Bose-Hubbard model. For strongly-interacting bosons, (i) additional MI phases appear, for which two (or more) atoms residing in {\it each site} undergo a Tonks-Girardeau-like transition and localize and (ii) on-site excitation becomes the excitation lowest in energy. Experimental implications are discussed.